The path of least impedance


I am sure most of you are familiar with the term Body Mass Index (BMI), and some of you may have even received one. Also, I am sure most of you are familiar with the controversy regarding the accuracy of BMIs. Unfortunately, BMI results do not accurately reflect the body fat percentage of certain populations, such as athletes and the elderly, because muscle mass is not taken into account [1]. For example, an athlete with significant muscle mass would report as overweight and an older individual lacking muscle mass would report as underweight [1]. In hopes of correcting the inaccuracies stemming from BMI calculations, bioelectrical impedance analysis (BIA) became a popular method for measuring body fat mass and body fat percentage.

With BIA, a small, alternating current is sent throughout the body and the impedance of electrical current to fat, water, and muscle content is recorded [2]. Fattier tissues will reduce the speed of electrical current whereas hydrated and muscular tissues will not [3]. Assuming that the body exists as a conductive cylinder uniform in material and density, allows for these impedance measurements to be easily converted into body composition measurements [4]. However, due to these assumptions, inaccuracies persist and an advantage of BIA over BMI remains unclear. BIA has the potential of providing more accurate and reliable results, but that must start with correcting the issues that result from its assumptions, more specifically its assumption that the body exists as a conductive cylinder.

Preliminary bioelectrical impedance analyzers made use of a one-cylinder model to make body composition measurements [5]. Unfortunately this method led to the underestimation of total body water, thus, leading to inaccurate results of body fat mass and lean body mass (Figure 1) [5]. To improve upon this issue, the 5-cylinder model was developed which makes cylinders out of the arms, legs, and trunk (Figure 1) [5]. In addition, the 5-cylinder model was able to expand upon its predecessor by providing detailed reports of each body part’s composition and whole-body composition [5].

Figure 1. Schematic of a one-cylinder model versus a 5-cylinder model [5].

In Calculus we learned that when approximating the area under the curve our estimation yields better results when we add more rectangles with smaller widths. Analogous to the previous scenario, our body composition measurements would prove to be more accurate by increasing the number of cylinders our body could model. Instead of using one cylinder, it may be more beneficial to have 5 cylinders.


To measure impedance among 5 cylinders requires more electrodes than the four that come with conventional BIA (Figure 2) [6]. Moreover, for the 5-cylinder model, all alternating current is supplied between the right ankle and right wrist [6]. To measure the potential difference of the upper limbs, lower limbs, and trunk, the electrodes are placed between the right and left wrist, right and left ankle, and left ankle and wrist, respectively [6]. All electrodes pairs are then attached to a four-channel, battery operated impedance instrument that reports the resistance, reactance, phase angle, and impedance [6].

Figure 2. 5-cylinder model electrode placement schematic [6].

In order to calculate impedance, the resistance, R, reactance, Xc, and phase angle must be known (Equation 1) [7]. Resistance is reflective of electrolyte-containing total body water in which lean muscles tend to have low resistance and fattier tissues tend to have a high resistance [7]. Reactance is reflective of body cell mass in which a higher proportion of cells gives rise to low reactance and a lower proportion of cells gives rise to a high reactance [7]. The phase angle readout is a component of the impedance instrument that allows for differentiation between resistance and reactance [7].

Z^2 = R^2 + Xc^2                        Equation 1

Now that we know how to calculate impedance, we must now relate impedance to total body water (TBW) shown in Equation 2 [6].

TBW = L^2/Z                            Equation 2

L: length of cylinder

Z: impedance of cylinder

To make use of these equations while maintaining full transparency, we must clarify the assumptions. Therefore, we assume:

  1. The supplied current follows the path of least resistance.
  2. The body is made up of segmental conductive cylinders [6].
  3. The total body water occupies a cylinder of length, L, and is uniform in resistivity (Equation 2) [6].

By assuming the path of least resistance we can exclude extraneous and complex equations that would otherwise be needed to solve for resistance. Secondly, by assuming segmental conductive cylinders, we can analyze a body part’s contribution to whole body impedance. Lastly, by assuming what is shown in Equation 2 we can again exclude extraneous and complex equations that would otherwise be needed to solve for TBW.


With this segmented approach, we can better estimate lean body mass (LBM) and fat mass (FM) by recording the individual lengths and resistivities of upper limb, lower limb, and trunk cylinders (Equation 3). Whereas for a one-cylinder model, the entire body was assumed to have one resistivity, which is inherently untrue considering the trunk and limbs distribute lean muscle and fat differently [6]. Unfortunately, even through a segmented approach of solving for TBW, reliability of Equation 2 is questionable which continues into Equation 3 [6]. Studies have shown that impedance, Z, contributes little to solving for lean body mass (LBM). Moreover, changes in impedance showed little to no change in LBM [6].

TBW = Lᵤₗ^2/Zᵤₗ + Lₗₗ^2/Zₗₗ + Lₜ^2/Zₜ                Equation 3

ul: upper limb

ll: lower limb

t: trunk

Despite its reliability being under question, we continue to make use of assumptions to simplify equations while maintaining some degree of accuracy. Moreover, now that we know TBW, we can solve for LBM and fat mass (FM) through the empirical estimations shown in Equation 5 and Equation 4 [7]. These empirical estimations are based on observations of human biological phenomena where on average a human’s lean body mass contains 73% of their total body water [7]. Because we are not all the same, deviations from Equation 4 do exist, which is a limitation of using empirical calculations.

LBM = TBW/0.73                        Equation 4

FM = Body Mass – LBM                    Equation 5

Although the segmental approach improves accuracy in comparison to the one-cylinder model, discrepancies still exist through the use of assumptions and empirical estimations. To further improve upon BIA, it is important that we rid of all empirical estimations and analyze impedance solely on the person. Fortunately, companies like InBody have made strides in improving this technology by minimizing the use of empirical estimations [5].


  1. Assessing Your Weight and Health Risk. NIH. Website. Accessed May 1, 2020.
  2. Grossi, M., Ricco, B. Electrical impedance spectroscopy (EIS) for biological analysis and food characterization: a review. J Sens Sens Syst. 2017; 6: 303-325.
  3. Bioelectrical Impedance Analysis (BIA). Science for Sport. Website. Published May 20, 2018. Accessed February 27, 2020.
  4. Dehghan, M., Merchant A.T. Is bioelectrical impedance accurate for use in large epidemiological studies? Nutr J. 2008; 7: 36. doi: 10.1186/1475-2891-7-26
  5. Revolutionizing BIA Technology with InBody. InBody. Website. Accessed May 12, 2020.
  6. Organ LW, Bradham GB, Gore DT, Lozier SL. Segmental bioelectrical impedance analysis: theory and application of a new technique. Journal of Applied Physiology. 1994 Jul; 77(1): 98-112.
  7. Bioelectrical Impedance Analysis (BIA) and Body Composition Analyse. DANTEST Media Inc. Website. Accessed May 12, 2020.


It’s Bioelectric! Boogie, Woogie, Woogie!

The Patent 

  • Patent title: Bioelectrical impedance measuring apparatus constructed by one-chip integrated circuit
  • Patent #: 6472888
  • Patent filing date: Jan. 29, 2001
  • Patent issue date: Oct. 29, 2002
  • How long it took for this patent to issue: 1yr and 9mo
  • Inventor(s): Oguma, Koji, Miyoshi, Tsutomu
  • Assignee: Tanita Corporation
  • US classification: 324/691; 324/692; 600/547
  • How many claims: 9

The Invention

Bioelectrical impedance apparatuses (BIA) estimate the body composition of the individual by sending a small electrical impulse through its tissues. The speed of this electrical current varies due to the water, muscle, and fat content in the tissues [1]. Tissues containing higher water and muscle content tend to have faster electrical currents, and thus, a lower impedance; whereas, tissues containing higher fat content tend to have slower electrical currents, and thus, a higher impedance [1]. Other factors, such as sex, height, and weight, are also considered when using this device. [2]

Having been available to the public since the 1980’s [1], this recent 2001 patent improves upon the original BIA by scaling down all the necessary processes onto a one-chip microcomputer [2]. The essential components of a BIA include: inputting patient information, applying electrical current, integrating bioelectrical impedance, and outputting one’s body composition, all of which remain withstanding [2]. The one-chip microcomputer is useful for 1) selectively generating and relaying an alternating-current (AC), 2) containing multiple switches that measure bioelectrical impedance, send the AC signal, and quantify the output voltage, and 3) containing devices that produce, supply, and detect voltage [2]. Overall, the inventors sought to maintain the effectiveness of the current solution whilst minimizing the amount of compartments needed to output one’s body composition.

Figure 1. Bioelectrical Impedance Analysis Schematic. The body is composed of fat or fat-free mass and water or water-free tissues (A) [8]. These different components result in different resistances, and thus, different impedances. Moving through water encounters less resistance than moving through fat (C) [8]. To measure impedance, the circuit connects to 2 electrodes placed at the wrist and 2 placed at the ankle (B) [8]. 

The Population

BIA can prove to be an effective tool for quantifying one’s body composition in clinical studies, more specifically studies whose population consists of individuals from developing countries [3] due to its low cost, portability, ease of use, and reliability [4]. Additionally, bioelectrical impedance analyzers are available for commercial use and offered from online retailers, such as Amazon [5]. Like an Apple Watch or Fitbit, one may resort to purchasing a BIA in means of receiving information regarding their body constitution in a timely fashion. Using an age limit similar to a Fitbit, individuals below the age of 13 should not make use of a BIA [6]. Moreover, the curiosity over one’s weight, body mass index, and body composition has been trending over the last decade, and is directly related to the booming health and fitness industry [7]. Aside from its current uses, BIA deems to be a probable technique for detecting the presence of abnormalities in the body (i.e. lesions and/or tumors) [2].

The Engineering

As previously stated, BIA relies on an electrical current that passes through various regions of high to low water, muscle, or fat content in order to decipher one’s body composition. This technique assumes the body exists as conductive cylinders, uniform in material and density, and fixed in cross-sectional area [3].In addition, BIA assumes that the body’s conductive volume is reflective of its water composition [3]. With these assumptions in mind, the formula that is used to estimate the contribution of a body part’s weight to the whole body resistance is as seen in equation 1.

V=p x S^2/R                (1)

The variable V represents the conductive volume; p represents the receptivity of the conductor; S represents the length of the conductor; and R represents the resistance of the cross-section area [3].

Two electrode configurations are used to measure four impedance values in the body – one from each electrode – and to decipher whether an anomaly has occurred [2]. The impedance analyzer makes use of a signal generator, sensor, switch, and drive and measurement electrodes in order to produce and measure a signal [2]. The principle behind Ohm’s Law (equation 2) is used to calculate the voltage difference between the two electrode configurations as current flows through the body [9]. For BIA measurements, electrodes are often placed at the wrist and ankle [9].

V=I x R                (2)

Impedance is the ratio between voltage and current, V/I, and is often represented as the variable, Z [9]. Moreover, Z is dependent upon resistance, R, and reactance, X, and can be expressed using the formula in equation 3.

Z=(R^2+X^2)^1/2            (3)

Engineers often use assumptions to simplify biological processes while also attempting to retain the maximum amount of information in said processes. Based on the assumptions that make up equations 1 and 3, researchers often encounter accuracy issues when analyzing BIA measurements [9]. To combat this, these equations can be manipulated so that they are only effective when the sample is reflective of its reference population’s impedance formula [9].

The Improvement

The one-chip microcomputer expands on prior solutions as it integrates all circuits that measure impedance onto a single platform. The inventors specifically compare their design to that of a body fat meter. In summary, the body fat meter makes use of a microcomputer, yet, continues to employ other instruments to calculate impedance, which results in 1) a large apparatus, 2) increased labor to create the circuit board, and 3) heightened likelihood of encountering noise [2]. In synopsis, the one-chip microcomputer allows for downsizing, offers a cheaper alternative, and reduces the margin for error. Additional patents use BIA to monitor abnormalities in the body [10], analyze organ output [11], or improve instrumentation of the device [12].

Figure 2. Patent Drawing. The above image displays the compartments needed to measure impedance on a one-chip microcomputer [2]. 


  1. Bioelectrical Impedance Analysis (BIA). Science for Sport. Website. Published May 20, 2018. Accessed February 27, 2020.
  2. Oguma, Koji, Miyoshi, Tsutomu. Bioelectrical impedance measuring apparatus constructed by one-chip integrated circuit. 2002.
  3. Dehghan, M., Merchant A.T. Is bioelectrical impedance accurate for use in large epidemiological studies? Nutr J. 2008; 7: 36. doi: 10.1186/1475-2891-7-26
  4. Essa’a, V.J., Dimodi, H.T., Ntsama, P.M. et al. Validation of anthropometric and bioelectrical impedance analysis (BIA) equations to predict total body water in a group of Cameroonian preschool children using deuterium dilution method. Nutrire. 2017; 42: 20.
  5. Bioelectrical Impedance Analysis. Amazon. Website. c1996-2020.  Accessed March 8, 2020.
  6. Terms of Service. Fitbit. Website. Updated September 18, 2018. Accessed March 8, 2020.
  7. The Six Reasons The Fitness Industry Is Booming. Forbes. Website. Published September 26, 2018. Accessed March 8, 2020.
  8. Grossi, M., Ricco, B. Electrical impedance spectroscopy (EIS) for biological analysis and food characterization: a review. J Sens Sens Syst. 2017; 6: 303-325.
  9. Bioelectrical Impedance Analysis in Body Composition Measurement. U.S. Department of Health & Human Services. Published December 12, 1994. Accessed March 8, 2020.
  10. Chetham, Scott, M. Apparatus for connecting impedance measurement apparatus to an electrode. 2014.
  11. Kaiser, Willi, Fideis, Martin. Apparatus and method for obtaining cardiac data. 2007.
  12. Chetham, Scott, Daly, Newton, C., Bruinsma, John, I. Measurement apparatus. 2016.


Achey Breaky Muscles

Athletic expertise is not required for one to feel the aching and lasting effects of delayed-onset muscle soreness (DOMS). The aftermath of these effects can often exist along a spectrum ranging from significant muscle tenderness to debilitating pain.¹ In addition, the duration of these effects can exist along a spectrum ranging from 24 to 72 hours.¹ A common misconception correlates a good workout with the subsequent symptoms of DOMS, however, that is just not the case. With that being said, DOMS will often occur in accord with performing new exercises or increasing the intensity and/or duration of a current exercise.¹


The lingering soreness and stiffness as a result of DOMS can often cause individuals to seek methods that will ultimately reduce these symptoms and accelerate their return to the gym. Unfortunately, many of the treatment options on the market have mixed outcomes due to the individualized nature of exercise. Some may obtain adequate results through methods, such as massage or ibuprofen, while others may not; whereas, some methods prove to be completely ineffective, such as cryotherapy and stretching.¹ Furthermore, let’s give a look at a newly proposed treatment for DOMS and whether its results are promising.


Blood-flow restriction (BFR) training is often used at physical therapy as a passive way to regain strength without adding heavy weight. The venous blood supply is terminated at the area of injury, which in turn reduces the amount of oxygen at the site, activates anaerobic metabolism, and encourages muscle hypertrophy.² This proves to be an effective technique for restrengthening the muscle of patients who strictly lift lighter loads.² But, where is the crossover between BFR and DOMS?

Figure 1. BFR machine.[8]

BFR is thought to provide an alternative training method that will achieve similar muscle gains to resistance training with heavy loads while also minimizing the effects of DOMS. It has been postulated that BFR training may attenuate DOMS by preventing calcium-mediated proteolysis³ and by recruiting fast-twitch motor units.⁴ However, it has also been hypothesized that BFR training may induce muscle damage through ischemia-reperfusion (lack of oxygen in the tissues) or through the reduction of neutrophils that aid in inflammatory response.⁵


A 2019 study wished to examine the effects of BFR training on DOMS by using 25 untrained females and submitting them to isokinetic forearm flexion training, where half performed a bicep curl with a BFR cuff at a load reflecting a 30% eccentric-peak torque and the other half at a load reflecting a 30% concentric-peak torque.⁶ The findings revealed neither eccentric or concentric movements with a BFR cuff resulted in DOMS after the 7 days of training.⁶ These results were inconsistent with other studies that showed an increase in DOMS with concentric exercises.⁶ Is this inconsistency due to the low number of participants, the lack of diversity, or the duration of the experiment being only 7 days?


In contrast, a 2017 study compared the effects of BFR training and resistance training on DOMS by using 17 male participants and assessing their elbow-flexor muscle strength for 7 days in one of four training techniques: heavy load, light load, intermittent high-pressure BFR, and continuous low-pressure BFR.⁷ From this, the researchers found DOMS was significantly greater in BFR training (both intermittent high-pressure and continuous low-pressure) than in resistance training (both in heavy and light load).⁷


Much like the other methods of muscle recovery, BFR training may not be the most effective way to minimize DOMS. Exercise can be highly variable and strongly impacted by genetics, which may be the reason a consistent and reliable technique for treating DOMS has yet to be discovered.


Watch this youtube video to learn more about DOMS.⁸

Questions to consider

  • Based on the study mentioned in this article, do you think their findings are an accurate representation of the effects of BFR training on DOMS?
  • How have your opinions regarding DOMS changed with this post?
  • Did the video help you understand DOMS in an easily digestible way?



  1. Cheung K, Hume P, Maxwell L. Delayed onset muscle soreness: treatment strategies and performance factors. Sports Med. 2003; 33(2):145-164. DOI: 10.2165/00007256-200333020-00005
  2. Blood-Flow Restriction Training. American Physical Therapy Association. Website. Updated May 24, 2019. Accessed February 20, 2020.
  3. Sudo M, Ando S, Poole DC, Kano Y. Blood flow restriction prevents muscle damage but not protein synthesis signaling following eccentric contractions. Physiol Rep. 2015;3(7):e12449.
  4. Loenneke JP, Fahs CA, Wilson JM, Bemben MG. Blood flow restriction: the metabolite/volume threshold theory. Med Hypotheses. 2011;77(5):748-752.
  5. Curty VM, et al. Blood flow restriction attenuates eccentric exercise-induced muscle damage without perceptual and cardiovascular overload. Clin Physiol Funct Imaging. 2017;38(3):468-476.
  6. Hill EC, Housh TJ, Smith CM, Keller JL, Schmidt RJ, Johnson GO. Eccentric and concentric blood flow restriction resistance training on indices of delayed onset muscle soreness in untrained women. Eur J Appl Physiol. 2019;119(10):2363-2373.
  7. Brandner CR, Warmington SA. Delayed onset muscle soreness and perceived exertion after blood flow restriction exercise. Journal of strength and conditioning research. 2017;31(11):3101-3108. doi:10.1519/JSC.0000000000001779
  8. Should You Still Train Sore? Youtube. Website. Published November 18, 2018. Accessed February 20, 2020.

Personalized Blood Flow Restriction. Owens Recovery Science. ORS. 2020c.